Part the Third

Amazon has a 12V lithium ion battery pack I'd used on other projects before; it comes with a charger and the price ($24) is pretty decent to get it next day. (Aliexpress has better pricing, but it can take weeks to get stuff from China).

For this application though, the battery pack required a bit of hacking. First off, there's a switch on the battery pack that must be on for the unit to operate, and that switch must also be in the on position to charge it. Not intuitive, in my opinion. It also has a battery gauge that reads out the charge level.

That LED level indicator is handy, but it is on all the time the battery pack is on. That would drain the battery pretty quick. So I opened up the pack, wired the rocker switch out of the circuit, and put the charge indicator on a momentary switch so it could be used to gauge the charge only when someone is actually looking to check the level.